Superposition Theorem

Superposition Theorem

This theorem is useful for those circuits that contain two or more than two sources. This theorem is applicable only when network or circuit contains with linear elements. The sources of emf connected only in parallel not in series. According to this theorem the current flowing through any section is the algebraic sum of all the currents which should flow in that section when each source of emf acts alone and all other sources are replaced by their internal resistances. In this article we will solve this theorem step by step and applications of superposition theorem.

Explanation of superposition theorem step by step

Consider a circuit which contains two emf source V1 and V2 and resistive elements R1, R2 and R3. You can see in figure 1.

Step 1

Take only one source V1 and replace the other source V2 by its internal resistance. If internal resistance is not given then it is taken as zero.

Note- If the circuit contains current source, we will delete the source from the circuit. In other words, we can say that the branch that contains current source which acts as a open circuit.

Arrow shows the direction of flow of current. Now determine the flow flowing through in various section of the circuit. The current is denoted by I1, I2 and I3.

Step 2.

Now take other emf’s source V2 and replace the source V1 resistance. Determine the current flowing in various section of the circuit. The current is denoted b I1” , I2” and I3”.
To determine the resultant current just odd the currents obtained in steps 1 and step 2. If the current obtained in step 1 and step 2 in same direction just add, on the other hand if the currents flowing through the circuit in opposite direction the it subtract them. In above explanation, currents flowing through resistance R1 and R2 is in opposite direction and in this case currents obtained by step 1 and step 2 are subtracted where as current flowing through resistance R3 is added.

As per superposition theorem

I1 = I1’ – I1”

I2 = I2’ – I2”

I3 = I3’ + I3”

Applications of superposition theorem

This theorem is applied for those circuits or networks that contains two or more than two current or voltage sources.

Limitations of Superposition Theorem

This theorem is applicable only for circuits or networks that contains only linear elements.